There is no email option on the log configuration or log viewer page. But the log configuration page has fields for "Server IP Address" and "Server UDP Port" and there is a help box on the side saying: If you have an external SYSLOG server, you may choose to configure external logging and all log entries will be sent to your remote server."
So with a little Googling, I found the free Kiwi Syslog Server and installed it on my PC So far, it looks like the DSL modem is actually talking to it, so that's good. It keeps a tab delimited log file on my local disk, which is what I was looking for.